So far we have focussed on detection of muons from below the horizon produced by muon neutrinos in the TeV-PeV regime, such as may be associated with GRB sources, AGN or other cosmic accelerators observed as TeV gamma-ray emitters. Neutrinos of both higher and lower energies can also be measured with IceCube. This capability will allow us to address other science that ranges from WIMP annihilation and supernova explosions to ντ appearance to neutrinos from topological defects of supermassive relic particles.
So far we have assumed an IceCube energy threshold of 0.4 TeV or higher. It is important to note that it will be possible to detect muon-neutrinos of significantly lower energy. If the track of the secondary muon is close to an individual string, its length can be deduced from the arrival times of Cherenkov photons detected by nearby PMTs. A good measurement requires nanosecond timing in several modules. Requiring, conservatively, signals in five modules separated by 17 m, the minimum tracklength is ∼ 70 m for a muon energy of ∼ 15 GeV. Requiring further that the distance from the string to the track is significantly less than the scattering length, 10 m for instance, yields a detection volume of 25 megaton with a threshold of less than 20 GeV for a source directly below the detector, in particular for neutrinos from annihilation of WIMPS trapped in the center of the Earth. For other directions the energy threshold is higher and the efficiency for a given energy is correspondingly lower. The cuts on track-length and proximity to a string can be relaxed if the detector would be exposed to an accelerator beam. During the short beam spills the detector is free of background and requirements on track measurement can be reduced thus increasing the target volume. On the other hand, the neutrino beam would be at some angle to the strings, depending on the location of the accelerator, which would reduce the acceptance.
Several science missions would benefit from a reduced threshold in a limited volume, e.g. the search for dark matter. If Weakly Interacting Massive Particles (WIMPs) make up the dark matter of the universe, they would also populate the galactic halo of our own Galaxy. They would be captured by the Earth or the Sun where they would annihilate pairwise, producing high-energy muon neutrinos that can be detected by neutrino telescopes. A favorite WIMP candidate is the lightest neutralino which arises in the Minimal Supersymmetric Model (MSSM). In general, IceCube's reach as a dark matter detector is complementary to that of direct search detectors because of its good sensitivity to larger neutralino masses, typically higher than a few hundred GeV. In addition, the rates depend on the capture and annihilation rates of the WIMPs in the Earth or Sun rather than their cross sections for interaction in the detector. High energy neutrinos produced in the annihilation of galactic neutralino dark matter have characteristic energies of 1/4 ∼ 1/6 the mass of the parent particles. A reduction in neutrino threshold therefore results in increased sensitivity to lower masses. The standard IceCube geometry presents an effective area of 0.7 km2 for WIMPs with mass = 50 GeV annihilating in the core of the Earth. For WIMPS in the Sun, because of the less favorable geometry, the effective area increases from ∼ .01 km2 for mw = 50 GeV and approaches 0.7 km2 for TeV WIMPS. The situation is most favorable for WIMPS above the threshold for decay into weak intermediate bosons, where IceCube is competitive with specialized future detectors such as GENIUS and CRESST in the search for neutralino dark matter anticipated in supersymmetric theories [45].
Another reason for maintaining sensitivity to ∼ 10 GeV neutrinos is that these may be produced in GRBs along with high energy neutrinos. Bahcall and Meszaros [46] have argued that a gamma-ray burst "fireball" is likely to contain an admixture of neutrons, in addition to protons, in essentially all progenitor scenarios. Inelastic collisions between protons and neutrons in the fireball produce muon neutrinos (antineutrinos) of ∼10 GeV energy as well as electron neutrinos (antineutrinos) of ∼5 GeV, which could produce ∼7 events/year in km-scale detectors, if the neutron abundance is comparable to that of protons. With a reduced threshold and exploiting coincidence in timing with the GRB, this flux may be observable.
A low threshold also preserves the capability discussed in connection with AMANDA (see sec. 12) to detect secondary muons from TeV-energy gamma rays produced in the atmosphere above the detector. These are guaranteed fluxes, calculable from the observed fluxes. The technique could be particularly revealing in GRB studies.
Neutrinos produced locally by interactions of cosmic-rays in the atmosphere constitute the foreground for neutrinos of astrophysical origin. They are both background and calibration source. The energy spectrum of atmospheric neutrinos is steep, falling approximately like E-3 and steepening to E-3.7 for E>>1 TeV. Above ∼ 10 GeV the flux of νe falls even more quickly, and above ∼ 100 effects of oscillations are also negligible. Thus atmospheric muon-neutrinos are a known calibration source up to a TeV and beyond. There is a characteristic factor of two excess of neutrinos from near the horizontal as compared to the vertical. Measuring the rate and angular dependence of atmospheric νμ-induced muons is therefore a benchmark measurement for IceCube.
The component of "prompt" νμ from charm decay has a harder spectrum than the component from decay of charged kaons and pions. It is expected to become the dominant source of atmospheric neutrinos above an energy of perhaps 100 TeV. The exact level of the prompt component is rather poorly known, and it could present a significant background for diffuse astrophysical neutrinos. If it is sufficiently large, it could be measured by IceCube as a hardening the neutrino energy spectrum by one power of the energy.
With a sufficiently low energy threshold, IceCube could also play a role in confirming the compelling indications that atmospheric neutrinos oscillate. Studies of systematics and backgrounds show, however, that significant progress would require smaller spacing of OMs along a string than presently planned. Such a specialized effort would be warranted only if ongoing experiments fail to prove oscillation of atmospheric neutrinos before IceCube construction.
The interactions of neutrinos with PeV energies and higher will have spectacular signatures in IceCube. (The simulated 6 PeV neutrino in fig. 16 illustrates this point.) Since the Earth becomes increasingly opaque to neutrinos with energy in the PeV range and higher, it is necessary to use events from horizontal and downgoing neutrinos. Fortunately, setting an energy threshold in the PeV energy region is high enough to be above atmospheric backgrounds. In this energy region the observed muon events in IceCube will be dominated by muon neutrinos interacting in the ice or atmosphere above the detector and near the horizon. PeV cascades from νe interactions in the detector volume also contribute at a somewhat lower rate. Tau neutrinos will also show up as cascades, as described below. Upgoing neutrinos are suppressed by an order of magnitude. Due to the Earth's opacity, the zenith angle distribution of neutrinos associated with EeV signals will have a striking signature. For a detailed discussion, see [36, 38].
With a threshold for cascades below the PeV region, IceCube will be complementary to detectors such as Auger, OWL and RICE which have thresholds of 10 EeV and higher. The lower threshold means that comparable event rates may be possible with IceCube even though its effective volume is much smaller.
The high-energy capability of IceCube will allow us to attack a major scientific problem, the existence of particles whose energy apparently exceeds the GZK cutoff. Speculations regarding their origin include heavy relics from the early Universe and topological defects which are remnant cosmic structures associated with phase transitions in grand unified gauge theories [30, 31, 32]. Interactions of ultra-high energy neutrinos with massive neutrinos in the galactic halo is also a possibility [33]. Such models would predict a sizeable flux of neutrinos in a much higher range of energy than the neutrinos associated with the GRB and AGN models mentioned above. Some limits on the highest predictions of neutrino fluxes are emerging from analysis of horizontal air showers, but there is still considerable phase space for exploration. Detection of neutrinos produced in interactions leading to the GZK cutoff is also a possibility, although their level is relatively low. Specific examples include:
Interest in detection of τ neutrinos is motivated by the evidence for neutrino oscillations from SuperKamiokande [39] and SNO [40]. Production of ντ in hadronic interactions or photoproduction is suppressed relative to νe and ντ by several orders of magnitude. In the absence of new physics, ντ of astrophysical origin would therefore be virtually undetectable. If, however, there is large mixing in the νμ↔ντ channel, then over astrophysical distances fluxes of ντ would be comparable to νμ.
Tau neutrinos of sufficiently high energy can in principle be identified in several ways in a km-scale neutrino detector. Perhaps the most striking signature would be the characteristic double bang events [41] in which the production and decay of a τ lepton would be seen as two separated bursts in the detector. It may also be possible to identify "lollipop" events in which a ντ with energy > PeV creates a long minimum-ionizing track that enters the detector and ends in a huge burst as the τ lepton decays to a final state with hadrons or an electron. The entering τ, because of its large mass, would emit fewer bremsstrahlung photons than a muon of similar energy. Such events would be detected from above or near the horizontal since the Earth is opaque to neutrinos with energies at or above the PeV region.
At still higher energies, the Earth becomes completely opaque to νe and νμ fluxes but it remains transparent to ντ flux [42]. In essence, ντ charged current interactions create a tau lepton, which decays before losing all its energy, and which always has a ντ as one of its decay products. This ultimately results in an upgoing ντ flux in the 100 TeV energy range. In what follows we discuss only the "double-bang" signature, which gives a conservative estimate of possible rates.
In a charged current ντ deep inelastic scattering (DIS) interaction with a nucleus, a τ lepton of energy (1-y)Eντ is produced as well as a hadronic shower of energy yEντ which is initiated in the fragmentation of the nucleus. Here y is the fraction of energy transferred to the hadronic vertex in the interaction. The τ lepton travels on average a distance Rτ along the medium before decaying given by:
| Rτ= | Eτ | ct0= | (1-y)Eντ | ct0 |
| mτ | mτ |
where Eτ and mτ are the energy and mass of the τ respectively and t0 is its rest lifetime. In its decay it produces another ντ and an electromagnetic or hadronic shower ∼; 82% of the times. Assuming a typical detector dimension D, there are several conditions that have to be fulfilled for the detection of a double bang event induced by aντ:
Using these criteria we can estimate the probability of detecting a double bang event in a neutrino telescope of linear dimension D = 1 km such as IceCube using a simple Monte Carlo. We take the energy threshold for detecting showers to be Eshower ∼ 1 TeV and fix 250 m as the minimum distance the τ has to travel to distinguish the Cherenkov light from both showers. This (conservative) number is mainly determined by the 125 m separation between strings since detection by separated strings is needed to establish the double burst for a horizontal event. This distance corresponds to a minimum energy of ∼ 5 PeV for the τ lepton. The requirement that both bursts occur inside the detector sets an upper limit of ∼ 20 PeV. With these constraints, one would expect at most a few events per year given current limits on neutrino fluxes from AMANDA. This conclusion is consistent with the result of Athar et al. [43], who find some tens of double bang events per year in the original AGN model [44] which is somewhat above current limits.
A high energy neutrino telescope in deep Antarctic ice is sensitive to the stream of low energy neutrinos produced by a galactic supernova Although 10-20 MeV energy is far below the AMANDA/IceCube trigger threshold, a supernova would be detected by higher counting rates in individual PMTs over a time window of 5-10 s. The enhancement in rate of a single PMT is buried in PMT dark noise. However, by summing the signals from all PMTs a significant excess would be observed. Limits obtained with AMANDA have been submitted for publication [47]. Relatively low background counting rates in ice (relative to water) make this possible.
Most of the energy released by a supernova is liberated in a burst lasting about ten seconds. Roughly equal energies are carried by each neutrino species with a thermal spectrum of temperature 2-4 MeV. Since the νe cross-section on protons in the detector is significantly larger than the interaction cross sections for the other neutrino flavors, νe events dominate the signal by a large factor after detection efficiency is taken into account. In this reaction, free protons absorb the antineutrino to produce a neutron and a positron which is approximately isotropically emitted with an energy close to that of the initial neutrino. A thermal spectrum of temperature 4 MeV, when folded with an inverse beta decay cross section which increases with the square of the neutrino energy, yields an observed positron energy distribution which peaks in the vicinity of 20 MeV. The track-length of a 20 MeV positron in ice is roughly 12 centimeters and therefore over 3000 Cherenkov photons are produced.
AMANDA and IceCube can contribute to the SuperNova Early Warning Network [48]. A recent analysis [47] shows that 70% of the galatic disk can be monitored for a supernova like SN1987A using a selected set of low noise AMANDA PMTs. Given a known template for time evolution of the pulse, the resulting accuracy in timing could be 14 ms for AMANDA-II and as good as 1-3 ms for IceCube. The resulting angular resolution depends on the orientation of the triangulation grid with respect to the supernova. The three detectors SuperK, SNO and IceCube will achieve typical resolution of 5 to 20 degrees. This is to be compared with the accuracy of about 5° achieved from the measured electron direction in a detector like SuperK.
Simultaneous detection of high energy and lower energy MeV neutrinos from a supernova is an exciting capability of a high energy neutrino telescope with supernova sensitivity. Loeb and Waxman [49] have shown that when a type II supernova shock breaks out of its progenitor star, it becomes collisionless and may accelerate protons to TeV-energy or higher. Inelastic nuclear collisions of these protons produce a ∼1 hr long flash of TeV neutrinos about 10 hr after the thermal neutrino burst from the cooling neutron star. A Galactic supernova in a red supergiant star would produce a neutrino flux of ∼ 10-4 erg/cm2 s. A km2 neutrino detector will detect ∼100 muons, thus allowing one to constrain both supernova models and neutrino properties. All these opportunities will be greatly enhanced by a low threshold associated with short tracks detected by individual strings.
